Using Engel Curves to Estimate Consumer Price Index Bias for the Elderly

By Gorry, James; Scrimgeour, Dean | Contemporary Economic Policy, July 2018 | Go to article overview

Using Engel Curves to Estimate Consumer Price Index Bias for the Elderly


Gorry, James, Scrimgeour, Dean, Contemporary Economic Policy


I. INTRODUCTION

We study the living standards of older Americans to determine how well consumer price index (CPI) changes reflect the cost of living. One claim about CPIs is that they understate the rate of increase of the cost of living for the elderly because the elderly consume a lot of health care, which is a sector that has seen faster than average price increases in recent decades (Hobijn and Lagakos 2005). A policy implication of this view is that cost of living adjustments (COLAs) should be made at a rate different from the CPI inflation rate (Hobijn and Lagakos 2003). An experimental index constructed by the Bureau of Labor Statistics suggests slightly higher inflation for retirees, 3.3% per year from 1982 to 2007 instead of 3.1% for all urban consumers (Stewart 2008).

Our approach to measuring changes in the cost of living for the elderly follows Costa (2001) and Hamilton (2001b), who analyze the Engel curve relationship between the food budget share and the total spending of the household. Costa and Hamilton use the drift over time in the Engel curve as an indirect measure of changes in the true cost of living and hence of real income. We estimate how much this drift varies depending on whether the household has an elderly head. A comparison of differential shifts in the Engel curves of older and younger Americans shows if CPI bias is a bigger problem for the elderly. Nominal income (or total expenditure) in the Engel curve is deflated by a price index that could have trend bias. This bias shows up in shifts in food Engel curves over time and an analysis of the bias allows for an estimation of the true rate of progress of living standards. Food Engel curves remain stable over time if deflated income and food prices are held constant among households with similar demographic characteristics. Any shifts in Engel curves are then seen as bias in the CPI.

There are several reasons why the CPI does not accurately measure changes in the cost of living. One source of bias is substitution. Substitution bias causes a Laspeyres index to overstate the inflation rate, and is one argument for indexation of social security payments to be based on a chain-type index that presumably does a better job of accounting for substitution (Cage, Greenlees, and Jackman 2003). Other reasons include the introduction of new goods, unmeasured quality improvements, and outlet bias. Refer Wynne and Sigalla (1996) or Hausman (2003) for more on these issues. See also the discussion of plutocratic and democratic weights by Pollak (1998) who observes that the market basket priced in the CPI reflects more closely the spending patterns of well-off households, rather than households near the middle of the income distribution.

Beatty and Crossley (2012) argue that the Engel curve method we use to estimate CPI bias is problematic due to differences in spending patterns between households across the income distribution. Engel curve drift estimates actual changes in the cost of living for one household, but the CPI measures changes in the cost of living for a different household. Therefore, differences could emerge if the inflation rate for these two households is generally different. We believe this critique is more relevant for studies that attempt to measure an overall bias in the CPI. By contrast, our study compares two groups of households, the elderly and nonelderly, and we are concerned with the bias of the CPI for one group in excess of the bias for the other group. The measurement problems highlighted by Beatty and Crossley (2012) are likely to be present for both groups and hence to be differenced out in our analysis. In addition, Hobijn and Lagakos (2005) find that the CPI inflation rate represents equally well changes in the cost of living for households at different parts of the income distribution over longer periods of time.

The Boskin Commission (Boskin et al. 1997, 1998) estimated that the CPI contained an annual upward bias of between 0. …

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